What gets me as a non-native speaker far more than "a vs an" is the "a vs the" conundrum. I still don't quite get when something needs to be "indefinite" and I've been speaking English for close to forty years. My native tongue lacks articles altogether and it's soo bloody hard I feel hopeless I'll ever master them fully.
As a Russian who's fluent in English, I feel like I ended up learning it mostly by example (Slavic languages lack articles, but we have other fun things for people learning them to trip up on, like cases). But a more general rule seems to be that it's "the" if you can point your finger at that particular thing or rephrase it with "that", otherwise it's "a".
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